Question

In the adjoining figure, the radius of the inner circles, if other circles are of radii m units is

• A. $(\sqrt{2}-1)m$
• B. $\sqrt{2}m$
• C. $\frac{1}{\sqrt{2}}m$
• D. $\frac{1}{\sqrt{2}+1}m$

Answer 1

Answer: (A)

$(\sqrt{2}-1)m$

Join the centres of the circles such that it forms a square and the centre of the inner circle lies on the diagonal of the square.
Now, each side will be 2m.
Hence, the diagonal of the square will be = $2\sqrt{2}m$
Length of the radius of inner circle = $\frac{2\sqrt{2}m-2m}{2}$
= $(\sqrt{2}-1)m$